Controllability scores of linear time-varying network systems

TL;DR

This paper extends the controllability score, a control theory-based network centrality measure, from linear time-invariant to linear time-varying systems, ensuring its uniqueness, continuity, and proposing a data-driven computation method.

Contribution

It introduces the extension of controllability scores to LTV systems, proves their uniqueness and continuity, and develops a data-driven approach for their computation.

Findings

Controllability scores are unique in almost all cases for LTV systems.

The proposed data-driven method effectively computes controllability scores.

Numerical experiments confirm the extension's validity and the method's performance.

Abstract

For large-scale network systems, network centrality based on control theory plays a crucial role in understanding their properties and controlling them efficiently. The controllability score is such a centrality index and can give a physically meaningful measure. It is originally proposed for linear time-invariant (LTI) systems, and we extend it to linear time-varying (LTV) systems in this paper. Since the controllability score is defined as an optimal solution to some optimization problem, it is not necessarily uniquely determined. Its uniqueness must be guaranteed for reproducibility and interpretability. In this paper, we show its uniqueness in almost all cases, which guarantees its use as a network centrality measure. We also prove its continuity with respect to the time parameters. In addition, we propose a data-driven method to compute it. Finally, we verify the effectiveness of the extension and examine the performance of the data-driven method through numerical experiments.